LIQUID PHASE EQUILIBRIUM OF A BINARY MIXTURE

A) Theoretical
	It was pointed out in the text "Boiling Point-Composition Diagram of a Binary Mixture" that positive deviation from Raoult's law (fi>1) was caused by the less attraction or/and more repulsion between particles of components 1 and 2 than between 1 and 1, 2 and 2 . The positive deviation may be of such extent that the homogeneous liquid separates into a two-phase liquid, that is the two components become partially immiscible. Component 1 is solvent and component 2 is solute in phase I while their role is opposite in phase II.
	This system has two components and three phases (vapor, liquid I, liquid II) so its degree of freedom (F=C-P+2=2-3+2) is 1. We focus our attention to the liquid I - liquid II subsystem considering it (practically) independent of vapor phase. We may do this since
		a) the volume of vapor phase is small, the amount of the components it 		    containes is negligible compared to their total amounts;
		b) change of molar volume (Vm) is very small, pressure has almost no 		    influence on equilibrium temperatures of liquid-liquid (or liquid-solid, 		    or solid-solid) phase transitions (remember Clapeyron's law)..
	Consequently, the only rational way is studying the temperature of phase transition as function of composition of the liquid phases.
	There is a general tendency at temperature changes: the higher it is  the weaker attractive forces between molecules are. One can expect that from a critical temperature (upper critical temperature of miscibility) liquid phase I and liquid phase II form a single liquid phase. Oppositely, if we decrease temperature and attracive forces in relation 1-2 strenghten more steeply than in relation 1-1 and 2-2, below a critical temperature (lower critical temperature of miscibility) a single liquid phase can be seen again.
	Clearly, a lower critical temperature does not exist for each immiscible liquid-pair. In addition, the upper critical temperature of miscibility could be higher than the boiling point and can not be observed. This is the case with a lower critical temperature if it was lower than the freezing point, too. Consequently, when measuring the equilibrium phase transition temperature-composition diagram of a partially immiscible liquid-pair one may observe
		a) no critical temperature at all;
		b) upper critical temperature of miscibility (Fig. 1. a),
		c) lower critical temperature of miscibility (Fig. 1. b);
		d) exceptionally, both upper and lower critical temperatures of 			    miscibility.

					Figure 1

	If  the temperature-composition point is in the two-phase region, the absolute or relative amount of a phase can be calculated with the lever rule (or balance rule):

					1)
		where 	ni, mi:		number of moles and mass of component i, 						respectively,
			xi, wi:		average mole fraction and mass fraction of the two 					phases for component i, respectively,
			xi,k ,wi,k:	mole fraction and mass fraction of component i in 					phase k, respectively.

B) Equipment
	There are serials of ampules of known average composition (mass fraction). Two ampules can be attached to a thermometer with a rubber ring. The thermometer with the ampules can be sunk into water being in an Erlenmeyer flask. (Figure 2)  There is an electric heater to raise the temperature of water if it is needed.

					Figure 2

C) Experimental
Systems having upper critical temperatures of miscibility are measured.
	1. Assemble the apparatus. 
	2. With continuous swirling, heat up water until the liquid in both ampules become homogeneous. Estimate roughly the temperatures of phase transitions.
	3. Cool water slowly with frequent swirling and read phase transition temperatures precisely. Measure them three times with repeated  heating and cooling.
	4. Change ampules for the next two ones and do procedures 2 and 3 again. 8-10 ampules should be measured for a phase diagram.
	5. Measure the phase transition temperature of an ampule with unknown mass fraction.
	6. Plot the measured temperatures versus average mass fractions (phase diagram).
Read the upper critical temperature of miscibility. Read mass fractions of liquid I and that of liquid II at a given temperature for the ampule measured under 5.